Update all but one result?

I'm trying to update a table to remove all but the first instance of a group. Basically, I have a table with vehicle data related to an insurance policy. Each policy should only have one power_unit. Everything else should be a towed unit. Unfortunately, a bug has been duplicating power units, and now I need to clean this up. There are ~10k records in the database, and ~4k of them have doubled up power units.

The important bits of my table (call it test1 for now) are:

+------------+---------+------+-----+---------+----------------+
| Field      | Type    | Null | Key | Default | Extra          |
+------------+---------+------+-----+---------+----------------+
| id         | int(10) | NO   | PRI | NULL    | auto_increment | 
| policy_id  | int(10) | NO   |     | NULL    |                | 
| power_unit | int(1)  | NO   |     | 0       |                | 
+------------+---------+------+-----+---------+----------------+

And some sample data:

+----+-----------+------------+
| id | policy_id | power_unit |
+----+-----------+------------+
|  1 |         1 |          1 | 
|  2 |         1 |          1 | 
|  3 |         1 |          1 | 
|  4 |         2 |          1 | 
|  5 |         2 |          1 | 
|  6 |         2 |          1 | 
|  7 |         4 |          1 | 
|  8 |         4 |          1 | 
|  9 |         4 |          1 | 
| 10 |         5 |          1 | 
| 11 |         5 |          1 | 
| 12 |         6 |          1 | 
+----+-----------+------------+

Basically I'd like to end up where policy_id 1 has only one power_unit=1. Same for policy_id 2, 3, 4, etc. For policy_id 6, nothing should change (there is only one entry, and it is a power_unit already).

I don't know if this is possible, but it was an intriguing problem for m开发者_Python百科e, so I thought you guys might find it the same.

Update:

I don't want to DELETE the rows, just UPDATE them to have power_unit=0.

---

UPDATE  test1 t1,
        (
        SELECT  policy, MIN(ti.id) AS mid
        FROM    test1 ti
        GROUP BY
                policy
        ) tm
SET     power_unit = 0
WHERE   t1.policy = tm.policy
        AND t1.id <> tm.mid;